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International Journal of Information Processing, 9(3), 76-91, 2015 ISSN : 0973-8215 IK International Publishing House Pvt. Ltd., New Delhi, India A Hybrid Fuzzy Firefly Based Evolutionary Radial Basis Functional Network for Classification H S Beheraa , M Nandaaa , K Nayakaa, Janmenjoy Nayakaa a Department of Computer Science Engineering and Information Technology, Veer Surendra Sai University of Technology (VSSUT) Burla, Sambalpur, Odisha-768018, India, E-mail: [email protected], [email protected], [email protected], [email protected] In this paper, a hybrid evolutionary fuzzy firefly based Radial Basis Function (RBF) network hasbeen designed to classify the real world data. The paper is comprised of two stages: first, the Fuzzy c-means (FCM) algorithm is applied with to get effective data points and then those data points have been inputted to the RBFN network for effective classification. The weights of RBF network are updated by using the firefly algorithm. The determination of centres of RBF units strongly affects the performance of a Radial Basis Function network. Various clustering algorithms like K-means and Fuzzy C-means algorithms are widely used to determine the location of centres of RBF units. But the traditional clustering algorithms like Fuzzy c-means algorithm and K-means algorithm are quite sensitive to initialization and they get trapped in the local optima. In order to enhance the performance of RBF network and to avoid the shortcomings of the traditional clustering techniques, a hybrid fuzzy clustering approach integrated with Firefly algorithm has been introduced in this study. The classification accuracy shows the effectiveness of the proposed method when compared with other methods in the literature. Keywords : Firefly, Fuzzy C-means, PSO, Radial Basis Functional Network. Generally a two phase learning strategy is carried out in the optimization of the RBFN parameters. The first phase includes the optimal estimation of the centres and widths of the RBF units by means of various strategies like clustering algorithms, decision trees, selforganizing maps etc. The second phase involves the optimization of connecting weights. This is accomplished by using traditional methods like Gradient Descent algorithms, Singular Value Decomposition (SVD) or Least Mean Squares (LMS) algorithms. During the learning process of a RBFN, the determination of the centres and the widths (kernel parameters) plays an important role in the improvement of the performance of the network. The estimation of the kernel parameters is a crucial and challenging problem, whereas the calculation of the connection weights is a standard process. 1. INTRODUCTION Artificial Neural Networks (ANNs) are computational models that mimic certain processing capabilities of neural cells present in human brain. ANNs have been widely used to solve many real life problems like pattern recognition, function approximation, classification, prediction and data processing. Radial Basis Function Networks (RBFNs) are special type of ANNs introduced by Broomhead and Lowe [1]. Because of their simpler and compact topology, faster learning algorithms, better approximation capabilities, RBFNs have been used in many engineering and scientific problems. Data classification is one of the major applications of the RBFNs. The learning process of a RBFN includes the optimization of three kinds of parameters: centres and widths of the RBF units as well as the connecting weights between the neurons. Fuzzy cluster analysis seems to be an efficient and promising tool to deal with this prob76 86 To compare the performance of our proposed method we have considered two other evolutionary methods which are FA-RBFN and PSO-RBFN. In case of FA-RBFN method all the parameters of the RBF network are optimized by means of the firefly algorithm simultaneously. So, a firefly is encoded as a combination of the centers, widths, and weights of the RBF network. In PSO-RBFN, all parameters of the network are optimized by the PSO algorithm. In this method, a particle is represented as a combination of the centers, widths, and weights of the RBF network. Here the objective function for both FA-RBFN and PSORBFN is to minimize the MSE of the RBF network. Tables 7 to Table 11 represent the classification accuracy of the data sets considered using the aforementioned methods. Table 12 compares the classification accuracy of our proposed method with other methods for the considered data sets. From the tables its clear that our proposed algorithm gives better results in terms of classification as compared to the other classification algorithms FA-RBFN and PSO- RBFN for the data sets considered. It can also be observed that our proposed method provides better results when compared with other existing methods from the described literatures. 6. CONCLUSIONS Now-a-days, researchers in various fields have been attracted towards the neural network research due to their vast applicability in diverse areas. In this study, an evolutionary learning strategy for constructing a data classifier using the radial basis function network, FCM and firefly algorithm have been proposed. The determination of kernel parameters in the RBFN has great significance in the performance of the network. A novel hybrid fuzzy clustering approach based on firefly algorithm was used to estimate the centres of the RBF units effectively and clustered the hidden units of the network efficiently. The connecting weights were also optimized by the help of firefly algorithm. H S Behera, et al.., To validate the performance of our proposed methodology many real world datasets are considered and the classification results revealed the superiority of the proposed method over the existing methods. From the comparative analysis and the obtained results indicate that the learning of RBFN by the proposed fuzzy method is quite promising and can be efficiently used in data classification task. In the near future, some other evolutionary or nature inspired optimizations techniques may be applied for the more accurate kernel parameter estimation of RBF network. Also, another direction of the work is the construction of new neurons or fuzzy neural architecture for various real world applications. REFERENCES 1. D S Broom head, Lowe and David. Radial Basis Functions, Multi-Variable Functional Interpolation and Adaptive Networks, (Technical Report) RSRE, pages 41–48, 1988. 2. A D Niros and G E Tsekouras. 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UCI Machine Learning Repository[http://archive.ics.uci.edu/ml], Irvine, CA: University of California, School of Information and Computer Science, 2013. Himansu Sekhar Behera is working as an Associate Professor in the Department of Computer Science Engineering and Information Technology, Veer Surendra Sai University of Technology (VSSUT), Burla, Odisha. His research interest includes Data Mining and Intelligent Computing. 91 M Nanda is a B.Tech research fellow in the Department of Computer Sc. Engineering & Information Technology, Veer Surendra Sai University of Technology (VSSUT), Burla, Odisha, India. K Nayak is a B.Tech research fellow in the Department of Computer Sc. Engineering & Information Technology, Veer Surendra Sai University of Technology (VSSUT), Burla, Odisha, India. Janmenjoy Nayak is a DST INSPIRE fellow in the Department of Computer Sc. Engineering and Information Technology, Veer Surendra Sai University of Technology (VSSUT), Burla, Odisha, India. His area of interest includes Data Mining, Artificial Intelligence, Pattern Recognition and Soft Computing.